{"count": 6, "status":"OK", "data":[{"pols": "[X^4, -4*(4*X+1)*(4*X+3)*(7*X^2+7*X+2), -128*(4*X+1)*(4*X+3)*(4*X+5)*(4*X+7)]", "text": "C*a", "degz": 2, "h3": "12", "sol": "1 24 4200 1034880 311711400 104849769024 37939351946496 14450910769152000 5718086730211026600 2330121882579042552000", "n_discr_factors": "2", "c3": "-228", "operator": "4 2 0 0 0 0 1 -24 -212 -660 -896 -448 -13440 -90112 -176128 -131072 -32768", "new_number": "2.3", "id": 33, "operator_tex": "\\theta^4-2^{2} x(4\\theta+1)(4\\theta+3)(7\\theta^2+7\\theta+2)-2^{7} x^{2}(4\\theta+1)(4\\theta+3)(4\\theta+5)(4\\theta+7)", "superseek": "52 220220", "discriminant": "2 1 -448 -32768", "aesz": "68", "n_sing_complex": "0", "inst_int": "", "c2h": "72", "hash": "13a48045ff0a42a9fcfbdb710baf1997", "dim_h": "8", "inst": " 52 2814 220220 29135058 4512922272 813434977450 159977765979708 33749653506239610 7496689709059170544 1735643559203414845168", "cleanlist": "True", "n_sing_real": "3", "sol_explicit": "A_{n}=\\dbinom{2n}{n}\\dbinom{4n}{2n}\\sum_{k=0}^{n}\\dbinom{n}{k}^3", "n_sing_rational": "3", "n_sing": "3", "laurent": null, "discriminant_tex": "-(64z+1)(512z-1)", "discr_factors": "-32768, z-1/512, z+1/64", "dm_basis": ["-1104893119/1000000000*I", "5", "1", "1", "-3", "-6", "-1", "0", "0", "12", "0", "0", "-12", "0", "0", "0"], "q": "0 1 -116 478 113008 -56372435 -6168706136 -1532666623214 -363738855142208 -89086162864734458", "yuk": "1 52 22564 5945992 1864666276 564115284052 175701961097704 54872373731039896 17279822597059346596 5465086797904141272568", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/64","im":"0","approx_re":"-0.015625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["4.+2.209786237*I","-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119*I","1+152*lambda","-.171535199-114*lambda","8","-3","8/3","-1-152*lambda","12","-6","5","-1.5000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000-1.104893119*I","24","-12","8","-2.-2.209786237*I"],"monodromy_dm":["-5","-24","-3","-2","3","13","3/2","1","-24","-96","-11","-8","18","72","9","7"]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":["1","-1","1/2","-1/6","0","1","-1","1/2","0","0","1","-1","0","0","0","1"],"monodromy_dm":["1","0","0","0","1","1","0","0","0","12","1","0","0","0","1","1"]},{"re":"1/512","im":"0","approx_re":"0.001953125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":["1.+1.104893119*I","0","57*lambda","276/2713","3","1","3/4","-57*lambda","0","0","1","0","12","0","3","1.-1.104893119*I"],"monodromy_dm":["1","-8","-1","-1","0","1","0","0","0","0","1","0","0","0","0","1"]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/4","3/4","5/4","7/4"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -35*X^4-70*X^3-63*X^2-28*X-5, (X+1)^2*(259*X^2+518*X+285), -225*(X+1)^2*(X+2)^2]", "text": "", "degz": 3, "h3": "120", "sol": "1 5 45 545 7885 127905 2241225 41467725 798562125 15855173825", "n_discr_factors": "3", "c3": "-80", "operator": "4 3 0 0 0 0 1 -5 -28 -63 -70 -35 285 1088 1580 1036 259 -900 -2700 -2925 -1350 -225", "new_number": "3.1", "id": 79, "operator_tex": "\\theta^4-x\\left(35\\theta^4+70\\theta^3+63\\theta^2+28\\theta+5\\right)+x^{2}(\\theta+1)^2(259\\theta^2+518\\theta+285)-3^{2} 5^{2} x^{3}(\\theta+1)^2(\\theta+2)^2", "superseek": "1 28/3", "discriminant": "3 1 -35 259 -225", "aesz": "34", "n_sing_complex": "0", "inst_int": "", "c2h": "120", "hash": "e5461c5f5ae4d929328f66b8955a31f5", "dim_h": "30", "inst": " 1 2 28/3 52 350 7852/3 21514 189154 5252815/3 16877300", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "4", "n_sing": "4", "laurent": null, "discriminant_tex": "-(z-1)(25z-1)(9z-1)", "discr_factors": "-225, z-1/25, z-1/9, z-1", "dm_basis": ["-80*lambda", "25", "1", "1", "-5", "-60", "-1", "0", "0", "120", "0", "0", "-120", "0", "0", "0"], "q": "0 1 -8 36 -168 514 -2760 1676 -83336 -498969", "yuk": "1 1 17 253 3345 43751 565613 7379303 96850193 1276434298", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/25","im":"0","approx_re":"0.04","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/9","im":"0","approx_re":"0.111111111111","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1","im":"0","approx_re":"1.0","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","2","2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, 8+32*X+44*X^2+24*X^3+96*X^4, -160+3344*X^4+32*X^3+368*X^2, 28544*X^4-155904*X^3-284800*X^2-267264*X-99328, -7036928-9865216*X^3-19801088*X^2-18862080*X-1442816*X^4, -53469184*X^4-293748736*X^3-641900544*X^2-642482176*X-249151488, -5247598592-12833783808*X-11946295296*X^2-4941938688*X^3-822607872*X^4, -46409973760*X^3-129895497728*X^2-153933053952*X-67398270976-6129975296*X^4, -1009686413312*X-491354324992-183341416448*X^3-717477642240*X^2-10099884032*X^4, -1469080141824+157840048128*X^4+496068722688*X^3-471372660736*X^2-2145336164352*X, 13258564042752*X^2+10617159155712*X+2638720532480+850403524608*X^4+6390911336448*X^3, 35596688949248*X+15427522527232+6047313952768*X^3+26938034880512*X^2-549755813888*X^4, -549755813888*(2*X+3)^4]", "text": "This is operator \"12.17\" from ...", "degz": 12, "h3": null, "sol": "1 -8 112 -1152 19216 -193664 3997440 -32147456 967568656 -3759626368", "n_discr_factors": "4", "c3": null, "operator": "4 12 0 0 0 0 1 8 32 44 24 96 -160 0 368 32 3344 -99328 -267264 -284800 -155904 28544 -7036928 -18862080 -19801088 -9865216 -1442816 -249151488 -642482176 -641900544 -293748736 -53469184 -5247598592 -12833783808 -11946295296 -4941938688 -822607872 -67398270976 -153933053952 -129895497728 -46409973760 -6129975296 -491354324992 -1009686413312 -717477642240 -183341416448 -10099884032 -1469080141824 -2145336164352 -471372660736 496068722688 157840048128 2638720532480 10617159155712 13258564042752 6390911336448 850403524608 15427522527232 35596688949248 26938034880512 6047313952768 -549755813888 -44530220924928 -118747255799808 -118747255799808 -52776558133248 -8796093022208", "new_number": "12.17", "id": 354, "operator_tex": "\\theta^4+2^{2} x\\left(24\\theta^4+6\\theta^3+11\\theta^2+8\\theta+2\\right)+2^{4} x^{2}\\left(209\\theta^4+2\\theta^3+23\\theta^2-10\\right)+2^{7} x^{3}\\left(223\\theta^4-1218\\theta^3-2225\\theta^2-2088\\theta-776\\right)-2^{10} x^{4}\\left(1409\\theta^4+9634\\theta^3+19337\\theta^2+18420\\theta+6872\\right)-2^{13} x^{5}\\left(6527\\theta^4+35858\\theta^3+78357\\theta^2+78428\\theta+30414\\right)-2^{17} x^{6}\\left(6276\\theta^4+37704\\theta^3+91143\\theta^2+97914\\theta+40036\\right)-2^{21} x^{7}\\left(2923\\theta^4+22130\\theta^3+61939\\theta^2+73401\\theta+32138\\right)-2^{24} x^{8}\\left(602\\theta^4+10928\\theta^3+42765\\theta^2+60182\\theta+29287\\right)+2^{26} x^{9}\\left(2352\\theta^4+7392\\theta^3-7024\\theta^2-31968\\theta-21891\\right)+2^{29} x^{10}\\left(1584\\theta^4+11904\\theta^3+24696\\theta^2+19776\\theta+4915\\right)-2^{35} x^{11}\\left(16\\theta^4-176\\theta^3-784\\theta^2-1036\\theta-449\\right)-2^{39} x^{12}\\left((2\\theta+3)^4\\right)", "superseek": "4 52", "discriminant": "12 1 96 3344 28544 -1442816 -53469184 -822607872 -6129975296 -10099884032 157840048128 850403524608 -549755813888 -8796093022208", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e65be092d4832d3740d2a3078755f447", "dim_h": null, "inst": " 4 7/2 52 500 2796 108891/2 523876 8014175 112614496 3281174301/2", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "8", "laurent": null, "discriminant_tex": "-(8z+1)(256z^2+16z-1)(1024z^3-160z^2-28z-1)^2(16z+1)^3", "discr_factors": "-8796093022208, (z^3-5/32*z^2-7/256*z-1/1024)^2, (z+1/16)^3, z^2+1/16*z-1/256, z+1/8", "dm_basis": null, "q": "0 1 0 -64 -256 -336 -3584 -161792 -3244032 -45146984", "yuk": "1 4 32 1408 32032 349504 11761664 179689472 4103289632 82095968992", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/8","im":"0","approx_re":"-0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32-1/32*5^(1/2)","im":"0","approx_re":"-0.101127","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/16","im":"0","approx_re":"-0.0625","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/192*(1187+6*3165^(1/2))^(1/3)-109/192/(1187+6*3165^(1/2))^(1/3)+5/96","im":"-1/8*3^(1/2)*(1/24*(1187+6*3165^(1/2))^(1/3)-109/24/(1187+6*3165^(1/2))^(1/3))","approx_re":"-0.057187","approx_im":"-0.018391","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/192*(1187+6*3165^(1/2))^(1/3)-109/192/(1187+6*3165^(1/2))^(1/3)+5/96","im":"1/8*3^(1/2)*(1/24*(1187+6*3165^(1/2))^(1/3)-109/24/(1187+6*3165^(1/2))^(1/3))","approx_re":"-0.057187","approx_im":"0.018391","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/32+1/32*5^(1/2)","im":"0","approx_re":"0.038627","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/96*(1187+6*3165^(1/2))^(1/3)+109/96/(1187+6*3165^(1/2))^(1/3)+5/96","im":"0","approx_re":"0.270624","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["3/2","3/2","3/2","3/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -152*X^4-200*X^3-212*X^2-112*X-24, 9872*X^4+25568*X^3+37776*X^2+28992*X+9376, -364032*X^4-1399808*X^3-2642176*X^2-2539008*X-1014016, 8529920*X^4+43130880*X^3+98770944*X^2+112343040*X+52101120, -135135232*X^4-830013440*X^3-2213789696*X^2-2879913984*X-1501495296, 1517879296*X^4+10569777152*X^3+31405178880*X^2+45223772160*X+25817448448, -12704546816*X^4-93967089664*X^3-293598134272*X^2-446554963968*X-269278511104, 83248545792*X^4+626159255552*X^3+1939722993664*X^2+2903272062976*X+1730242674688, -436207616000*X^4-3331284008960*X^3-10178669838336*X^2-14365726081024*X-7823954018304, 1791001362432*X^4+13958643712000*X^3+44105019162624*X^2+63200443760640*X+33853200662528, -5634997092352*X^4-43843026157568*X^3-140393890971648*X^2-210762635149312*X-122007135977472, 13194139533312*X^4+107752139522048*X^3+340298848796672*X^2+490931941801984*X+272060408397824, -1099511627776*(2*X+5)^4]", "text": "This is operator \"13.3\" from ...", "degz": 13, "h3": null, "sol": "1 24 464 8832 178960 4010368 100357376 2772019200 82738408720 2613822935424", "n_discr_factors": "4", "c3": null, "operator": "4 13 0 0 0 0 1 -24 -112 -212 -200 -152 9376 28992 37776 25568 9872 -1014016 -2539008 -2642176 -1399808 -364032 52101120 112343040 98770944 43130880 8529920 -1501495296 -2879913984 -2213789696 -830013440 -135135232 25817448448 45223772160 31405178880 10569777152 1517879296 -269278511104 -446554963968 -293598134272 -93967089664 -12704546816 1730242674688 2903272062976 1939722993664 626159255552 83248545792 -7823954018304 -14365726081024 -10178669838336 -3331284008960 -436207616000 33853200662528 63200443760640 44105019162624 13958643712000 1791001362432 -122007135977472 -210762635149312 -140393890971648 -43843026157568 -5634997092352 272060408397824 490931941801984 340298848796672 107752139522048 13194139533312 -687194767360000 -1099511627776000 -659706976665600 -175921860444160 -17592186044416", "new_number": "13.3", "id": 371, "operator_tex": "\\theta^4-2^{2} x\\left(38\\theta^4+50\\theta^3+53\\theta^2+28\\theta+6\\right)+2^{4} x^{2}\\left(617\\theta^4+1598\\theta^3+2361\\theta^2+1812\\theta+586\\right)-2^{8} x^{3}\\left(1422\\theta^4+5468\\theta^3+10321\\theta^2+9918\\theta+3961\\right)+2^{11} x^{4}\\left(4165\\theta^4+21060\\theta^3+48228\\theta^2+54855\\theta+25440\\right)-2^{14} x^{5}\\left(8248\\theta^4+50660\\theta^3+135119\\theta^2+175776\\theta+91644\\right)+2^{16} x^{6}\\left(23161\\theta^4+161282\\theta^3+479205\\theta^2+690060\\theta+393943\\right)-2^{20} x^{7}\\left(12116\\theta^4+89614\\theta^3+279997\\theta^2+425868\\theta+256804\\right)+2^{23} x^{8}\\left(9924\\theta^4+74644\\theta^3+231233\\theta^2+346097\\theta+206261\\right)-2^{27} x^{9}\\left(3250\\theta^4+24820\\theta^3+75837\\theta^2+107033\\theta+58293\\right)+2^{28} x^{10}\\left(6672\\theta^4+52000\\theta^3+164304\\theta^2+235440\\theta+126113\\right)-2^{32} x^{11}\\left(1312\\theta^4+10208\\theta^3+32688\\theta^2+49072\\theta+28407\\right)+2^{36} x^{12}\\left(192\\theta^4+1568\\theta^3+4952\\theta^2+7144\\theta+3959\\right)-2^{40} x^{13}\\left((2\\theta+5)^4\\right)", "superseek": "4 52", "discriminant": "13 1 -152 9872 -364032 8529920 -135135232 1517879296 -12704546816 83248545792 -436207616000 1791001362432 -5634997092352 13194139533312 -17592186044416", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "9127ce057848ca38f220a7bb67e245a2", "dim_h": null, "inst": " 4 7/2 52 500 2796 108891/2 523876 8014175 112614496 3281174301/2", "cleanlist": "True", "n_sing_real": "6", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "8", "laurent": null, "discriminant_tex": "-(1-48z+256z^2)(8z-1)^2(512z^3-32z^2+20z-1)^2(16z-1)^3", "discr_factors": "-17592186044416, (z^3-1/16*z^2+5/128*z-1/512)^2, 1/256-3/16*z+z^2, (z-1/8)^2, (z-1/16)^3", "dm_basis": null, "q": "0 1 -16 192 -2304 24240 -254976 2316288 -22216704 157621400", "yuk": "1 4 32 1408 32032 349504 11761664 179689472 4103289632 82095968992", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(64+3*3165^(1/2))^(1/3)+29/96/(64+3*3165^(1/2))^(1/3)+1/48","im":"-1/8*3^(1/2)*(1/12*(64+3*3165^(1/2))^(1/3)+29/12/(64+3*3165^(1/2))^(1/3))","approx_re":"0.005863","approx_im":"-0.196043","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/96*(64+3*3165^(1/2))^(1/3)+29/96/(64+3*3165^(1/2))^(1/3)+1/48","im":"1/8*3^(1/2)*(1/12*(64+3*3165^(1/2))^(1/3)+29/12/(64+3*3165^(1/2))^(1/3))","approx_re":"0.005863","approx_im":"0.196043","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32-1/32*5^(1/2)","im":"0","approx_re":"0.023873","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/48*(64+3*3165^(1/2))^(1/3)-29/48/(64+3*3165^(1/2))^(1/3)+1/48","im":"0","approx_re":"0.050774","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","0","-1","1"],"monodromy":[],"monodromy_dm":[]},{"re":"3/32+1/32*5^(1/2)","im":"0","approx_re":"0.163627","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["5/2","5/2","5/2","5/2"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -80*X^4-136*X^3-116*X^2-48*X-8, 2000*X^4+5792*X^3+7536*X^2+4544*X+1056, -24448*X^4-77568*X^3-109440*X^2-75264*X-19712, 196608*X^4+565248*X^3+575488*X^2+274432*X+50176, -1097728*X^4-3112960*X^3-3055616*X^2-1015808*X-24576, 3997696*X^4+9830400*X^3+11337728*X^2+6094848*X+1245184, -9961472*X^4-26214400*X^3-29360128*X^2-16252928*X-3670016, 8388608*(X+1)^4]", "text": "This is operator \"8.69\" from ...", "degz": 8, "h3": null, "sol": "1 8 128 2816 74896 2247808 73109504 2514939904 90124906768 3331662028928", "n_discr_factors": "4", "c3": null, "operator": "4 8 0 0 0 0 1 -8 -48 -116 -136 -80 1056 4544 7536 5792 2000 -19712 -75264 -109440 -77568 -24448 50176 274432 575488 565248 196608 -24576 -1015808 -3055616 -3112960 -1097728 1245184 6094848 11337728 9830400 3997696 -3670016 -16252928 -29360128 -26214400 -9961472 8388608 33554432 50331648 33554432 8388608", "new_number": "8.69", "id": 517, "operator_tex": "\\theta^4-2^{2} x\\left(20\\theta^4+34\\theta^3+29\\theta^2+12\\theta+2\\right)+2^{4} x^{2}\\left(125\\theta^4+362\\theta^3+471\\theta^2+284\\theta+66\\right)-2^{7} x^{3}\\left(191\\theta^4+606\\theta^3+855\\theta^2+588\\theta+154\\right)+2^{10} x^{4}\\left(192\\theta^4+552\\theta^3+562\\theta^2+268\\theta+49\\right)-2^{13} x^{5}\\left(134\\theta^4+380\\theta^3+373\\theta^2+124\\theta+3\\right)+2^{16} x^{6}\\left(61\\theta^4+150\\theta^3+173\\theta^2+93\\theta+19\\right)-2^{19} x^{7}\\left(19\\theta^4+50\\theta^3+56\\theta^2+31\\theta+7\\right)+2^{23} x^{8}\\left((\\theta+1)^4\\right)", "superseek": "4 52", "discriminant": "8 1 -80 2000 -24448 196608 -1097728 3997696 -9961472 8388608", "aesz": null, "n_sing_complex": "2", "inst_int": "", "c2h": null, "hash": "e303d10e77a367612be2fb706f37b895", "dim_h": null, "inst": " 4 15/2 52 1563/2 7276 210627/2 1572452 97434231/4 409802336 14179335317/2", "cleanlist": "True", "n_sing_real": "5", "sol_explicit": "", "n_sing_rational": "3", "n_sing": "7", "laurent": null, "discriminant_tex": "(16z-1)(8z-1)(64z^2-48z+1)(1-4z+32z^2)^2", "discr_factors": "8388608, z-1/8, z^2-3/4*z+1/64, z-1/16, (1/32-1/8*z+z^2)^2", "dm_basis": null, "q": "0 1 -16 160 -1536 10512 -79872 128512 -3670016 -65954024", "yuk": "1 4 64 1408 50080 909504 22749184 539351040 12471631648 298745904352", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8-1/4*2^(1/2)","im":"0","approx_re":"0.021447","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"-1/16*7^(1/2)","approx_re":"0.0625","approx_im":"-0.165359","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"0","approx_re":"0.0625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/16","im":"1/16*7^(1/2)","approx_re":"0.0625","approx_im":"0.165359","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/8","im":"0","approx_re":"0.125","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"3/8+1/4*2^(1/2)","im":"0","approx_re":"0.728553","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1","1","1","1"],"monodromy":[],"monodromy_dm":[]}]}, {"pols": "[X^4, -736*X^4-896*X^3-700*X^2-252*X-36, 166656*X^4+463872*X^3+473472*X^2+204672*X+33840, -4460544*X^4-64364544*X^3-99846144*X^2-49600512*X-9061632, -2448949248*X^4-927203328*X^3+8059944960*X^2+6023282688*X+1332412416, 146087608320*X^4+582312001536*X^3-2463105024*X^2-160271695872*X-49304567808, 11529369944064*X^4-10078006542336*X^3-11015685144576*X^2-1638899122176*X+467820085248, -146767085568*(2*X+1)*(1336*X^3+2772*X^2+2234*X+663), -84537841287168*(2*X+1)*(4*X+3)*(4*X+5)*(2*X+3)]", "text": "This is operator \"8.78\" from ...", "degz": 8, "h3": null, "sol": "1 36 3780 555120 95199300 17826144336 3532282505136 728151261963840 154550955916302660 33549072371964349200", "n_discr_factors": "3", "c3": null, "operator": "4 8 0 0 0 0 1 -36 -252 -700 -896 -736 33840 204672 473472 463872 166656 -9061632 -49600512 -99846144 -64364544 -4460544 1332412416 6023282688 8059944960 -927203328 -2448949248 -49304567808 -160271695872 -2463105024 582312001536 146087608320 467820085248 -1638899122176 -11015685144576 -10078006542336 11529369944064 -97306577731584 -522490824622080 -1062593699512320 -1009757548707840 -392161652637696 -3804202857922560 -18260173718028288 -30771774228529152 -21641687369515008 -5410421842378752", "new_number": "8.78", "id": 527, "operator_tex": "\\theta^4-2^{2} x\\left(184\\theta^4+224\\theta^3+175\\theta^2+63\\theta+9\\right)+2^{4} 3 x^{2}\\left(3472\\theta^4+9664\\theta^3+9864\\theta^2+4264\\theta+705\\right)-2^{8} 3^{2} x^{3}\\left(1936\\theta^4+27936\\theta^3+43336\\theta^2+21528\\theta+3933\\right)-2^{16} 3^{3} x^{4}\\left(1384\\theta^4+524\\theta^3-4555\\theta^2-3404\\theta-753\\right)+2^{19} 3^{4} x^{5}\\left(3440\\theta^4+13712\\theta^3-58\\theta^2-3774\\theta-1161\\right)+2^{22} 3^{5} x^{6}\\left(11312\\theta^4-9888\\theta^3-10808\\theta^2-1608\\theta+459\\right)-2^{26} 3^{7} x^{7}(2\\theta+1)(1336\\theta^3+2772\\theta^2+2234\\theta+663)-2^{32} 3^{9} x^{8}(2\\theta+1)(4\\theta+3)(4\\theta+5)(2\\theta+3)", "superseek": "52 48732", "discriminant": "8 1 -736 166656 -4460544 -2448949248 146087608320 11529369944064 -392161652637696 -5410421842378752", "aesz": null, "n_sing_complex": "3", "inst_int": "", "c2h": null, "hash": "2fb524ad6efb19e0117ae7acbd9f67b9", "dim_h": null, "inst": " 52 -399 48732 -992750 98106208 -13164377111/3 346622274844 -20762287104686 1625571068932672 -109698228104560776", "cleanlist": "True", "n_sing_real": "4", "sol_explicit": "", "n_sing_rational": "2", "n_sing": "7", "laurent": null, "discriminant_tex": "-(256z-1)(110592z^3+6912z^2-288z+1)(-1+96z+13824z^2)^2", "discr_factors": "-5410421842378752, z^3+1/16*z^2-1/384*z+1/110592, z-1/256, (-1/13824+1/144*z+z^2)^2", "dm_basis": null, "q": "0 1 -108 7662 -522608 37550709 -2726199720 203058824274 -15495782553792 1207671346097154", "yuk": "1 52 -3140 1315816 -63539140 12263276052 -947833839368 118891440271544 -10630291061138372 1185041309253233704", "gv2": null, "gv0": null, "gv1": null, "spectrum":[{"re":"-1/192*(-36+12*I*3^(1/2))^(1/3)-1/16/(-36+12*I*3^(1/2))^(1/3)-1/48+1/96*I*3^(1/2)*(1/2*(-36+12*I*3^(1/2))^(1/3)-6/(-36+12*I*3^(1/2))^(1/3))","im":"0","approx_re":"-0.091906","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/288-1/288*7^(1/2)","im":"0","approx_re":"-0.012659","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"0","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["0","0","0","0"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/192*(-36+12*I*3^(1/2))^(1/3)-1/16/(-36+12*I*3^(1/2))^(1/3)-1/48-1/96*I*3^(1/2)*(1/2*(-36+12*I*3^(1/2))^(1/3)-6/(-36+12*I*3^(1/2))^(1/3))","im":"0","approx_re":"0.00385","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"1/256","im":"0","approx_re":"0.00390625","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"-1/288+1/288*7^(1/2)","im":"0","approx_re":"0.005714","approx_im":"0.0","exponents":["0","1","3","4"],"monodromy":[],"monodromy_dm":[]},{"re":"1/96*(-36+12*I*3^(1/2))^(1/3)+1/8/(-36+12*I*3^(1/2))^(1/3)-1/48","im":"0","approx_re":"0.025556","approx_im":"0.0","exponents":["0","1","1","2"],"monodromy":[],"monodromy_dm":[]},{"re":"infinity","im":"0","approx_re":"0.0","approx_im":"0.0","exponents":["1/2","3/4","5/4","3/2"],"monodromy":[],"monodromy_dm":[]}]}]}